If you have the resources and time to invest in your own personal garden, then this could definitely cut down costs on your food bill. Having fresh herbs, vegetables and fruits at hand to create healthy meals is convenient. The internet is a fantastic source of all things related to gardening and there are many communities online willing to help the novice gardener.
Growing your own food is cost beneficial as long as you're decent at it! If you have one good harvest, even if your space is small, the amount of money it took to take care of that little bit of space will be made up by what you get out of it. But if you let yourself slack on the upkeep, or your soil and weather just isn't good, then you might not get anything in the end.
There is an initial outlay to prepare garden beds and buy the supplies you need, but over time you get that money back. Once you have broken even, it is close to pure cost savings to grown your own food. Lettuce might seem cheap at the store, but you can use parts of used heads to plant again, so you have a never ending supply. Same with other foods.
Growing all of your own food is not cost beneficial. Yes, growing some of your food can save you a little money. However, growing food requires a lot of time and hard work. Furthermore, many climates require constant watering in summer months which can significantly increase your water bill. This can make growing a lot of your own food costly.